Grooveshark’s road to streaming music popularity has been a bumpy one. Of the big-name services that you can still sign up for, it’s arguably the one that’s faced the most legal adversity. Now, Grooveshark is facing another challenge: an anti-piracy group in Denmark is seeking a court-ordered DNS block.

The Rettigheds Alliancen recently won a battle which forced Danish internet providers to block The Pirate Bay. With that matter now settled in their favor, the Alliance has set its sights on taking down Grooveshark.

So why would a rights group lump Grooveshark in with a torrent tracker like The Pirate Bay? Unlike competitors like Spotify, MOG, and Rdio, Grooveshark doesn’t have all its licensing deals in place. While the lack of label cooperation didn’t pose a significant roadblock to Amazon or Google when they both launched cloud music lockers earlier this year, Grooveshark is more than a private locker. And since you can stream (or cache offline) possibly unlicensed songs, that’s why Grooveshark has irked the Alliance.

Curiously, it seems as though Grooveshark has the capability to block certain artists from appearing in its listings. You’ll be hard pressed to find songs by Smashing Pumpkins or Lenny Kravitz, for example. Indeed, Grooveshark has historically cooperated with DMCA takedown requests. But the Danish group says that dealing with Grooveshark has proved “impossible” and that they don’t have the patience to stick to those protocols any longer.

Pressure from rightsholders has worked against Grooveshark before — right here in the U.S., where it was booted from the Android Market despite not clearly violating any of the Market’s terms of service. It’s too bad that listening to your favorite songs online has to be so complicated in 2011. Maybe we should all start passing around mix tapes again.